Volkswagen of America said on Thursday it is creating an independent claims program for the owners of nearly 600,000 diesel vehicles that emit up to 40 times legally allowable emissions.

The German automaker said it is naming compensation expert Ken Feinberg, who administered compensation funds for the 9/11 attacks, the BP Deepwater Horizon oil spill and General Motors ignition-switch crashes, to create and administer the program.

Discovered earlier this year to be rigging its autos with emissions-cheatng software, VW has acknowledged that 482,000 2.0-liter 2009-2015 diesel cars and 85,000 3.0-liter SUVs and larger cars have higher-than-allowed emissions. As a result, the automaker faces more than 500 lawsuits and a U.S. Justice Department investigation.

VW said Feinberg "will develop an independent, fair and swift process for resolving these claims."

VW Group of America President and CEO Michael Horn said Feinberg's "extensive experience in handling such complex matters will help to guide us as we move forward to make things right with our customers."

Feinberg said he will "commence work immediately designing an independent claims process that will meet claimants' needs." He added that "we hope to have a claims program designed as expeditiously as possible."

VW is still awaiting approval of fixes for the vehicles and has a stop sale on 2016 diesel vehicles.